On Which Graphs Are All Random Walks in Random Environments Transient?
نویسندگان
چکیده
An infinite graph G has the property that a random walk in random environment on G defined by i.i.d. resistances with any common distribution is almost surely transient, if and only if for some p < 1, simple random walk is transient on a percolation cluster of G under bond percolation with parameter p.
منابع مشابه
A PRELUDE TO THE THEORY OF RANDOM WALKS IN RANDOM ENVIRONMENTS
A random walk on a lattice is one of the most fundamental models in probability theory. When the random walk is inhomogenous and its inhomogeniety comes from an ergodic stationary process, the walk is called a random walk in a random environment (RWRE). The basic questions such as the law of large numbers (LLN), the central limit theorem (CLT), and the large deviation principle (LDP) are ...
متن کاملRandom Walks on Directed Covers of Graphs
Directed covers of finite graphs are also known as periodic trees or trees with finitely many cone types. We expand the existing theory of directed covers of finite graphs to those of infinite graphs. While the lower growth rate still equals the branching number, upper and lower growth rates do not longer coincide in general. Furthermore, the behaviour of random walks on directed covers of infi...
متن کاملRecurrence Theorems in Various Types of Random Walk
In 1921 George Polya famously resolved the question of recurrence versus transience of the simple random walk on integer lattices. In this talk we will study the analogous question for random basic walks, which are random processes related to the problem of graph exploration by a mobile entity. After discussing recurrence results on other generalizations of simple random walks, we’ll resolve th...
متن کاملTransient random walks on a strip in a random environment
We consider transient random walks on a strip in a random environment. The model was introduced by Bolthausen and Goldsheid in [4]. We derive a strong law of large numbers for the random walks in a general ergodic setup and obtain an annealed central limit theorem in the case of uniformly mixing environments. In addition, we prove that the law of the “environment viewed from the position of the...
متن کاملProbabilistic Self-Stabilization and Biased Random Walks on Dynamic Graphs
A distributed system is said to be probabilistic self-stabilizing, if it eventually converges to a legitimate computation with probability 1, starting from any global configuration. Like a self-stabilizing system, a probabilistic self-stabilizing system tolerates any number of transient failures and recovers a legitimate computation, but only probabilistically, unlike a self-stabilizing system,...
متن کامل